We know that certain there was a crystal in the novels that has shown time warping abilities

Perhaps from all the data Cortana has downloaded from the Halos, she has figured out how to reliably transport herself through time. Much like how in First Strike she was able to make covenant weapons work much more efficiently; maybe she was able to solve the problems of time travel as well, all she needs is a covenant ship and a crystal.

All this data from Halo's control room may have also given her the key to her own sustainability, preventing her demise; in a sense making herself immortal.

Cortana, with possibly the help of half jaw or arby, is able to get into the systems of a Covenant ship and take it back in time. Her love of humanity is so strong, that she waits eons for the covenant to find her. When they do find her, they think she is a gift from the Gods, and so begins her attempts to effectively destroy the covenant.

Perhaps it was Cortana that prevented the Covenant from being innovative. Maybe she intentionally weakened their technology. Perhaps she created the Covenant's AI to be so weak that she herself can crack them when her younger self comes into contact with them in First Strike.

Could it be possible that all of the Covenant's military blunders (albeit only a few) be attributed to Cortana?

Could it also be possible that Cortana stalled the covenant's discovery of the Halos until humanity had the technology (slipspace, MAC guns, Spartans) to possibly stand a chance?

And now, Cortana could be on the Forerunner ship, and will be able to help the MC out in Halo 3?